Question

Statistics approximating the mean of a data set given a frequency distribution

Answer 1

- The mean formula is given as:

`\begin{gathered} \bar{x}=\sum_(i=1)^n(fix_i)/(f_i) \\ \\ where, \\ x_i=\text{ The ith data point} \\ f_i=\text{ The frequency of the ith data point} \end{gathered}`

- Thus, we can find the mean as follows:

`\begin{gathered} \text{ We have been told to use the midpoint of the classes. Thus, we can say:} \\ x_i=\lbrace3,8,13,18,23,28\rbrace \\ fi=\lbrace22,21,15,9,4,3\rbrace \\ \\ \text{ Thus, the mean commute distance for students is:} \\ \bar{x}=(3(22)+8(21)+13(15)+18(9)+23(4)+28(3))/(22+21+15+9+4+3) \\ \\ \bar{x}=(767)/(74) \\ \\ \bar{x}=10.36486486...\approx10.4\text{ \lparen To 1 decimal place\rparen} \end{gathered}`

Final Answer

The mean distance is 10.4 miles